What are the coordinates of the vertex for f (x) = 3x^2+6x+3

The x-coordinate of the vertex can be found by - b/2a where the equation is ax^2 + bx + c

3x^2 + 6x + 3

b is 6, and a is 3

-b/2a = - 6/2 (3) = - 6/6 = - 1

The x-coordinate of the vertex is - 1. To find the y-coordinate plug the x-coordinate into the equation and solve for y.

f (-1) = 3 (-1) ^2 + 6 (-1) + 3

= 3 (1) - 6 + 3

= 3 - 6 + 3

= 0

The y-coordinate is 0

The vertex is (-1, 0)